Azure Active Directory (Azure AD) and Active Directory Domain Services (AD DS) are both identity and access management solutions from Microsoft, but they serve different purposes.

AD DS is the traditional on-premises directory service used to manage and authenticate users, computers, and other resources in a Windows domain network. It provides centralized management of objects in a domain, including authentication and authorization services, and can be used to manage access to on-premises resources such as files, folders, and applications. Azure AD, on the other hand, is a cloud-based directory service that provides identity and access management capabilities for cloud-based and on-premises resources.

It allows users to authenticate and access cloud-based services and applications using their existing corporate credentials, such as their username and password. Azure AD can also be used to manage access to resources outside of the organization's network, including SaaS applications and other cloud-based services.

While AD DS is primarily used for on-premises directory services, Azure AD is focused on providing identity and access management for cloud-based resources. However, it's important to note that Azure AD can also integrate with on-premises AD DS, allowing for a hybrid identity solution that extends on-premises directory services to the cloud.